{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "google",
   "metadata": {},
   "source": [
    "##### Copyright 2023 Google LLC."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "apache",
   "metadata": {},
   "source": [
    "Licensed under the Apache License, Version 2.0 (the \"License\");\n",
    "you may not use this file except in compliance with the License.\n",
    "You may obtain a copy of the License at\n",
    "\n",
    "    http://www.apache.org/licenses/LICENSE-2.0\n",
    "\n",
    "Unless required by applicable law or agreed to in writing, software\n",
    "distributed under the License is distributed on an \"AS IS\" BASIS,\n",
    "WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
    "See the License for the specific language governing permissions and\n",
    "limitations under the License.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "basename",
   "metadata": {},
   "source": [
    "# 3_jugs_regular"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "link",
   "metadata": {},
   "source": [
    "<table align=\"left\">\n",
    "<td>\n",
    "<a href=\"https://colab.research.google.com/github/google/or-tools/blob/main/examples/notebook/contrib/3_jugs_regular.ipynb\"><img src=\"https://raw.githubusercontent.com/google/or-tools/main/tools/colab_32px.png\"/>Run in Google Colab</a>\n",
    "</td>\n",
    "<td>\n",
    "<a href=\"https://github.com/google/or-tools/blob/main/examples/contrib/3_jugs_regular.py\"><img src=\"https://raw.githubusercontent.com/google/or-tools/main/tools/github_32px.png\"/>View source on GitHub</a>\n",
    "</td>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "doc",
   "metadata": {},
   "source": [
    "First, you must install [ortools](https://pypi.org/project/ortools/) package in this colab."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "install",
   "metadata": {},
   "outputs": [],
   "source": [
    "%pip install ortools"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "description",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "  3 jugs problem using regular constraint in Google CP Solver.\n",
    "\n",
    "  A.k.a. water jugs problem.\n",
    "\n",
    "  Problem from Taha 'Introduction to Operations Research',\n",
    "  page 245f .\n",
    "\n",
    "  For more info about the problem, see:\n",
    "  http://mathworld.wolfram.com/ThreeJugProblem.html\n",
    "\n",
    "  This model use a regular constraint for handling the\n",
    "  transitions between the states. Instead of minimizing\n",
    "  the cost in a cost matrix (as shortest path problem),\n",
    "  we here call the model with increasing length of the\n",
    "  sequence array (x).\n",
    "\n",
    "  Compare with other models that use MIP/CP approach,\n",
    "  as a shortest path problem:\n",
    "  * Comet: http://www.hakank.org/comet/3_jugs.co\n",
    "  * Comet: http://www.hakank.org/comet/water_buckets1.co\n",
    "  * MiniZinc: http://www.hakank.org/minizinc/3_jugs.mzn\n",
    "  * MiniZinc: http://www.hakank.org/minizinc/3_jugs2.mzn\n",
    "  * SICStus: http://www.hakank.org/sicstus/3_jugs.pl\n",
    "  * ECLiPSe: http://www.hakank.org/eclipse/3_jugs.ecl\n",
    "  * ECLiPSe: http://www.hakank.org/eclipse/3_jugs2.ecl\n",
    "  * Gecode: http://www.hakank.org/gecode/3_jugs2.cpp\n",
    "\n",
    "\n",
    "  This model was created by Hakan Kjellerstrand (hakank@gmail.com)\n",
    "  Also see my other Google CP Solver models:\n",
    "  http://www.hakank.org/google_or_tools/\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "code",
   "metadata": {},
   "outputs": [],
   "source": [
    "from ortools.constraint_solver import pywrapcp\n",
    "from collections import defaultdict\n",
    "\n",
    "#\n",
    "# Global constraint regular\n",
    "#\n",
    "# This is a translation of MiniZinc's regular constraint (defined in\n",
    "# lib/zinc/globals.mzn), via the Comet code refered above.\n",
    "# All comments are from the MiniZinc code.\n",
    "# '''\n",
    "# The sequence of values in array 'x' (which must all be in the range 1..S)\n",
    "# is accepted by the DFA of 'Q' states with input 1..S and transition\n",
    "# function 'd' (which maps (1..Q, 1..S) -> 0..Q)) and initial state 'q0'\n",
    "# (which must be in 1..Q) and accepting states 'F' (which all must be in\n",
    "# 1..Q).  We reserve state 0 to be an always failing state.\n",
    "# '''\n",
    "#\n",
    "# x : IntVar array\n",
    "# Q : number of states\n",
    "# S : input_max\n",
    "# d : transition matrix\n",
    "# q0: initial state\n",
    "# F : accepting states\n",
    "\n",
    "\n",
    "def regular(x, Q, S, d, q0, F):\n",
    "\n",
    "  solver = x[0].solver()\n",
    "\n",
    "  assert Q > 0, 'regular: \"Q\" must be greater than zero'\n",
    "  assert S > 0, 'regular: \"S\" must be greater than zero'\n",
    "\n",
    "  # d2 is the same as d, except we add one extra transition for\n",
    "  # each possible input;  each extra transition is from state zero\n",
    "  # to state zero.  This allows us to continue even if we hit a\n",
    "  # non-accepted input.\n",
    "\n",
    "  # Comet: int d2[0..Q, 1..S]\n",
    "  d2 = []\n",
    "  for i in range(Q + 1):\n",
    "    row = []\n",
    "    for j in range(S):\n",
    "      if i == 0:\n",
    "        row.append(0)\n",
    "      else:\n",
    "        row.append(d[i - 1][j])\n",
    "    d2.append(row)\n",
    "\n",
    "  d2_flatten = [d2[i][j] for i in range(Q + 1) for j in range(S)]\n",
    "\n",
    "  # If x has index set m..n, then a[m-1] holds the initial state\n",
    "  # (q0), and a[i+1] holds the state we're in after processing\n",
    "  # x[i].  If a[n] is in F, then we succeed (ie. accept the\n",
    "  # string).\n",
    "  x_range = list(range(0, len(x)))\n",
    "  m = 0\n",
    "  n = len(x)\n",
    "\n",
    "  a = [solver.IntVar(0, Q + 1, 'a[%i]' % i) for i in range(m, n + 1)]\n",
    "\n",
    "  # Check that the final state is in F\n",
    "  solver.Add(solver.MemberCt(a[-1], F))\n",
    "  # First state is q0\n",
    "  solver.Add(a[m] == q0)\n",
    "  for i in x_range:\n",
    "    solver.Add(x[i] >= 1)\n",
    "    solver.Add(x[i] <= S)\n",
    "\n",
    "    # Determine a[i+1]: a[i+1] == d2[a[i], x[i]]\n",
    "    solver.Add(\n",
    "        a[i + 1] == solver.Element(d2_flatten, ((a[i]) * S) + (x[i] - 1)))\n",
    "\n",
    "\n",
    "def main(n):\n",
    "\n",
    "  # Create the solver.\n",
    "  solver = pywrapcp.Solver('3 jugs problem using regular constraint')\n",
    "\n",
    "  #\n",
    "  # data\n",
    "  #\n",
    "\n",
    "  # the DFA (for regular)\n",
    "  n_states = 14\n",
    "  input_max = 15\n",
    "  initial_state = 1  # 0 is for the failing state\n",
    "  accepting_states = [15]\n",
    "\n",
    "  ##\n",
    "  # Manually crafted DFA\n",
    "  # (from the adjacency matrix used in the other models)\n",
    "  ##\n",
    "  # transition_fn =  [\n",
    "  #    # 1  2  3  4  5  6  7  8  9  0  1  2  3  4  5\n",
    "  #     [0, 2, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0],  # 1\n",
    "  #     [0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],  # 2\n",
    "  #     [0, 0, 0, 4, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0],  # 3\n",
    "  #     [0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],  # 4\n",
    "  #     [0, 0, 0, 0, 0, 6, 0, 0, 9, 0, 0, 0, 0, 0, 0],  # 5\n",
    "  #     [0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0],  # 6\n",
    "  #     [0, 0, 0, 0, 0, 0, 0, 8, 9, 0, 0, 0, 0, 0, 0],  # 7\n",
    "  #     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15], # 8\n",
    "  #     [0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0], # 9\n",
    "  #     [0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0], # 10\n",
    "  #     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0], # 11\n",
    "  #     [0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13, 0, 0], # 12\n",
    "  #     [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0], # 13\n",
    "  #     [0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15], # 14\n",
    "  #                                                     # 15\n",
    "  #     ]\n",
    "\n",
    "  #\n",
    "  # However, the DFA is easy to create from adjacency lists.\n",
    "  #\n",
    "  states = [\n",
    "      [2, 9],  # state 1\n",
    "      [3],  # state 2\n",
    "      [4, 9],  # state 3\n",
    "      [5],  # state 4\n",
    "      [6, 9],  # state 5\n",
    "      [7],  # state 6\n",
    "      [8, 9],  # state 7\n",
    "      [15],  # state 8\n",
    "      [10],  # state 9\n",
    "      [11],  # state 10\n",
    "      [12],  # state 11\n",
    "      [13],  # state 12\n",
    "      [14],  # state 13\n",
    "      [15]  # state 14\n",
    "  ]\n",
    "\n",
    "  transition_fn = []\n",
    "  for i in range(n_states):\n",
    "    row = []\n",
    "    for j in range(1, input_max + 1):\n",
    "      if j in states[i]:\n",
    "        row.append(j)\n",
    "      else:\n",
    "        row.append(0)\n",
    "    transition_fn.append(row)\n",
    "\n",
    "  #\n",
    "  # The name of the nodes, for printing\n",
    "  # the solution.\n",
    "  #\n",
    "  nodes = [\n",
    "      '8,0,0',  # 1 start\n",
    "      '5,0,3',  # 2\n",
    "      '5,3,0',  # 3\n",
    "      '2,3,3',  # 4\n",
    "      '2,5,1',  # 5\n",
    "      '7,0,1',  # 6\n",
    "      '7,1,0',  # 7\n",
    "      '4,1,3',  # 8\n",
    "      '3,5,0',  # 9\n",
    "      '3,2,3',  # 10\n",
    "      '6,2,0',  # 11\n",
    "      '6,0,2',  # 12\n",
    "      '1,5,2',  # 13\n",
    "      '1,4,3',  # 14\n",
    "      '4,4,0'  # 15 goal\n",
    "  ]\n",
    "\n",
    "  #\n",
    "  # declare variables\n",
    "  #\n",
    "  x = [solver.IntVar(1, input_max, 'x[%i]' % i) for i in range(n)]\n",
    "\n",
    "  #\n",
    "  # constraints\n",
    "  #\n",
    "  regular(x, n_states, input_max, transition_fn, initial_state,\n",
    "          accepting_states)\n",
    "\n",
    "  #\n",
    "  # solution and search\n",
    "  #\n",
    "  db = solver.Phase(x, solver.INT_VAR_DEFAULT, solver.INT_VALUE_DEFAULT)\n",
    "\n",
    "  solver.NewSearch(db)\n",
    "\n",
    "  num_solutions = 0\n",
    "  x_val = []\n",
    "  while solver.NextSolution():\n",
    "    num_solutions += 1\n",
    "    x_val = [1] + [x[i].Value() for i in range(n)]\n",
    "    print('x:', x_val)\n",
    "    for i in range(1, n + 1):\n",
    "      print('%s -> %s' % (nodes[x_val[i - 1] - 1], nodes[x_val[i] - 1]))\n",
    "\n",
    "  solver.EndSearch()\n",
    "\n",
    "  if num_solutions > 0:\n",
    "    print()\n",
    "    print('num_solutions:', num_solutions)\n",
    "    print('failures:', solver.Failures())\n",
    "    print('branches:', solver.Branches())\n",
    "    print('WallTime:', solver.WallTime(), 'ms')\n",
    "\n",
    "  # return the solution (or an empty array)\n",
    "  return x_val\n",
    "\n",
    "\n",
    "# Search for a minimum solution by increasing\n",
    "# the length of the state array.\n",
    "for n in range(1, 15):\n",
    "  result = main(n)\n",
    "  result_len = len(result)\n",
    "  if result_len:\n",
    "    print()\n",
    "    print('Found a solution of length %i:' % result_len, result)\n",
    "    print()\n",
    "    break\n",
    "\n"
   ]
  }
 ],
 "metadata": {},
 "nbformat": 4,
 "nbformat_minor": 5
}
